We can get monopole $1/r$, dipole $1/r^2$, quadrupole $1/r^3$ and octupole $1/r^4$ potential falloff by placing opposite point charges at the corners of a point, line, square and cube, respectively. ...

I am currently working on my bachelor's thesis on the anapole / toroidal moment and it seems that I am stuck with a tensor decomposition problem.
I have actually never had a course about tensors, so ...

I am wondering why a spin-S particle have only the term up to $k=2S$ in his multipole expansion ?
It seems that the Wigner-Eckart theorem shows the relation between spin and multipole expansion but I ...

I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, ...